Run One Full Lap and Your Average Velocity Is Exactly Zero
Learn to describe position from a reference point, tell distance from displacement, calculate average speed and average velocity separately, and find acceleration with its direction.
How can you run 400 metres and have zero average velocity?
Because velocity is calculated from displacement, and one full lap brings you back to where you started.
Suppose a runner completes one lap of a m circular track in s.
The distance covered is the whole path length, m, so
The displacement is the straight line from start to finish — and since the finish is the start, it is zero. So
The runner was moving the whole time, and nothing about that is contradicted. Average velocity simply answers a different question: not how fast were you going? but how fast did your position change?
Sorting out which quantity a question asks for is most of the work in this topic. This page covers the first part of the CBSE Class 9 Science chapter on describing motion.
Suppose a runner completes one lap of a m circular track in s.
The distance covered is the whole path length, m, so
The displacement is the straight line from start to finish — and since the finish is the start, it is zero. So
The runner was moving the whole time, and nothing about that is contradicted. Average velocity simply answers a different question: not how fast were you going? but how fast did your position change?
Sorting out which quantity a question asks for is most of the work in this topic. This page covers the first part of the CBSE Class 9 Science chapter on describing motion.
Why do you need a reference point to describe position?
Because position has no meaning on its own — only relative to something else.
To state where an object is, you need a reference point (also called the origin), a direction taken as positive, and a distance. Together these make a coordinate axis.
Worked example. Take a tree as the reference point and east as positive. Then:
- A lamp post m east of the tree is at position m
- A bench m west of the tree is at position m
The sign carries the direction, which is all a single axis needs. The distance between the lamp post and the bench is m.
Motion is relative too. A passenger sitting in a moving bus is at rest with respect to the bus and in motion with respect to the road. Both statements are correct, because they use different reference points, and neither is more true than the other.
Everyday evidence. Sitting in a stationary train beside another train that starts to move, you feel for a moment as though your own train is moving. Your eyes took the neighbouring train as the reference point, and relative to it you genuinely were moving.
**So an object is in motion is an incomplete statement.** It needs with respect to what? to be answered. A book on a table is at rest relative to the table, and moving at enormous speed relative to the Sun.
Choosing the reference point is yours to do. Nothing in physics prefers one over another, and the whole of this page becomes easier if you fix the origin and the positive direction in a single line before starting — because from that point onwards, signs do all the work of describing direction.
To state where an object is, you need a reference point (also called the origin), a direction taken as positive, and a distance. Together these make a coordinate axis.
Worked example. Take a tree as the reference point and east as positive. Then:
- A lamp post m east of the tree is at position m
- A bench m west of the tree is at position m
The sign carries the direction, which is all a single axis needs. The distance between the lamp post and the bench is m.
Motion is relative too. A passenger sitting in a moving bus is at rest with respect to the bus and in motion with respect to the road. Both statements are correct, because they use different reference points, and neither is more true than the other.
Everyday evidence. Sitting in a stationary train beside another train that starts to move, you feel for a moment as though your own train is moving. Your eyes took the neighbouring train as the reference point, and relative to it you genuinely were moving.
**So an object is in motion is an incomplete statement.** It needs with respect to what? to be answered. A book on a table is at rest relative to the table, and moving at enormous speed relative to the Sun.
Choosing the reference point is yours to do. Nothing in physics prefers one over another, and the whole of this page becomes easier if you fix the origin and the positive direction in a single line before starting — because from that point onwards, signs do all the work of describing direction.
How can distance and displacement be different for the same journey?
Distance is the whole path travelled; displacement is the straight line from start to finish, with a direction.
- Distance is a scalar — magnitude only, always positive, and it can never decrease during a journey
- Displacement is a vector — magnitude and direction, and it can be zero or negative
Worked example 1 — a turn. Walk m east, then m north.
The displacement is the straight line closing the right-angled triangle:
directed north-east of the starting point. Notice that — the shortcut is always shorter than the path.
Worked example 2 — a reversal. Walk m east, then m west.
The m walked back adds to the distance and subtracts from the displacement — a single journey in which the two quantities move in opposite directions.
Worked example 3 — a complete lap. One lap of a m track gives a distance of m and a displacement of zero.
Worked example 4 — a longer journey. A bus travels km north and then km east.
Everyday evidence. A taxi meter charges you for distance, because that is what the wheels turned through. A map app tells you the displacement when it says a place is km away as the crow flies, and then quotes a longer road distance separately.
The rule that constrains every answer. Distance is never less than the magnitude of displacement. They are equal only when the motion is in a straight line without reversing, and in every other case the distance is greater. So an answer with a displacement larger than the distance is wrong before anything else is checked.
- Distance is a scalar — magnitude only, always positive, and it can never decrease during a journey
- Displacement is a vector — magnitude and direction, and it can be zero or negative
Worked example 1 — a turn. Walk m east, then m north.
The displacement is the straight line closing the right-angled triangle:
directed north-east of the starting point. Notice that — the shortcut is always shorter than the path.
Worked example 2 — a reversal. Walk m east, then m west.
The m walked back adds to the distance and subtracts from the displacement — a single journey in which the two quantities move in opposite directions.
Worked example 3 — a complete lap. One lap of a m track gives a distance of m and a displacement of zero.
Worked example 4 — a longer journey. A bus travels km north and then km east.
Everyday evidence. A taxi meter charges you for distance, because that is what the wheels turned through. A map app tells you the displacement when it says a place is km away as the crow flies, and then quotes a longer road distance separately.
The rule that constrains every answer. Distance is never less than the magnitude of displacement. They are equal only when the motion is in a straight line without reversing, and in every other case the distance is greater. So an answer with a displacement larger than the distance is wrong before anything else is checked.
Formula
How do you calculate average speed and average velocity?
Both are measured in metres per second, written or . Speed is a scalar; velocity is a vector and needs a direction stated.
The unit conversion to know.
So km/h m/s, km/h m/s, and km/h m/s. To go the other way, multiply by .
Worked example 1 — the reversal journey. A person walks m east in s, then m west in s.
One journey, two different answers, and both are correct.
Worked example 2 — the trap. A car covers km in h, then km in h. Find its average speed.
The two stage speeds are km/h and km/h. The average speed is not their average:
Averaging and would have given km/h, which is wrong. Average speed is always total distance over total time, and averaging the individual speeds is only correct in the special case where the two stages take equal times — which here they do not.
Worked example 3 — in metres per second. Convert that answer: m/s.
Worked example 4 — uniform and non-uniform motion. An object covering equal distances in equal intervals of time is in uniform motion, and then its speed at every instant equals its average speed. If the distances in equal intervals differ, the motion is non-uniform and the average tells you nothing about any particular instant.
Everyday evidence. A car's speedometer shows instantaneous speed — what it is doing right now. Dividing a journey's total distance by its total time gives the average, and the two agree only if the car held one steady speed throughout, which almost never happens in traffic.
State the direction for a velocity. *Average velocity m/s is an incomplete answer; m/s east* is complete. Marks are given for the direction, and leaving it off treats a vector as a scalar.
How do you find average acceleration and its direction?
Divide the change in velocity by the time taken.
where is the initial velocity and the final velocity. The unit is metres per second squared, — a change of velocity per second.
Worked example 1 — speeding up. A car starts from rest and reaches m/s in s.
in the direction of motion. Each second, the car gains m/s of velocity.
Worked example 2 — slowing down. A bus travelling at m/s slows to m/s in s.
The negative sign means the acceleration is opposite to the direction of motion. This is often called a retardation of , but it is not a separate quantity — it is simply negative acceleration.
Worked example 3 — with a unit conversion. A train speeds up from km/h to km/h in s.
Convert first: m/s and m/s.
Convert before substituting. Putting km/h values into the formula and then calling the answer is wrong by a factor of , and it is the commonest arithmetic error in this section.
Acceleration points along the change in velocity, not along the velocity. A car moving east while slowing down has an acceleration pointing west, because its velocity is changing westward. So an accelerating object need not be speeding up, and a slowing object is still accelerating.
Zero acceleration means constant velocity, not zero velocity. A car cruising steadily at m/s has while moving quite fast; a car at a red light has and, while stationary, also . Those are two different situations with the same acceleration.
A boundary case that matters later. An object going round a circle at constant speed is still accelerating, because its direction — and therefore its velocity — is changing every instant. Speed is not enough to decide whether something is accelerating, and that case is taken up in the third part of this chapter.
where is the initial velocity and the final velocity. The unit is metres per second squared, — a change of velocity per second.
Worked example 1 — speeding up. A car starts from rest and reaches m/s in s.
in the direction of motion. Each second, the car gains m/s of velocity.
Worked example 2 — slowing down. A bus travelling at m/s slows to m/s in s.
The negative sign means the acceleration is opposite to the direction of motion. This is often called a retardation of , but it is not a separate quantity — it is simply negative acceleration.
Worked example 3 — with a unit conversion. A train speeds up from km/h to km/h in s.
Convert first: m/s and m/s.
Convert before substituting. Putting km/h values into the formula and then calling the answer is wrong by a factor of , and it is the commonest arithmetic error in this section.
Acceleration points along the change in velocity, not along the velocity. A car moving east while slowing down has an acceleration pointing west, because its velocity is changing westward. So an accelerating object need not be speeding up, and a slowing object is still accelerating.
Zero acceleration means constant velocity, not zero velocity. A car cruising steadily at m/s has while moving quite fast; a car at a red light has and, while stationary, also . Those are two different situations with the same acceleration.
A boundary case that matters later. An object going round a circle at constant speed is still accelerating, because its direction — and therefore its velocity — is changing every instant. Speed is not enough to decide whether something is accelerating, and that case is taken up in the third part of this chapter.
Exam tip
Exam tip: read whether the question wants speed or velocity
Decide first whether the question needs distance or displacement. Speed and average speed use distance; velocity and average velocity use displacement.
**Average speed ** — never the average of the two speeds. km in h plus km in h gives km/h, not .
State the direction of every velocity, displacement and acceleration. A vector answer without a direction is incomplete.
Convert km/h to m/s before substituting: multiply by , so km/h m/s and km/h m/s. Multiply by to go back.
Distance is never less than the magnitude of displacement, and they are equal only for motion in a straight line without reversing. Use that as a check.
For a closed path, displacement is zero, so average velocity is zero while average speed is not.
A negative acceleration is just acceleration opposite to the motion — write *retardation of or acceleration of *, and do not treat them as different things.
Acceleration lies along the change in velocity, so a slowing car accelerates backwards.
Zero acceleration means constant velocity, not being at rest.
And write the unit on every answer: m/s for speed and velocity, for acceleration.
**Average speed ** — never the average of the two speeds. km in h plus km in h gives km/h, not .
State the direction of every velocity, displacement and acceleration. A vector answer without a direction is incomplete.
Convert km/h to m/s before substituting: multiply by , so km/h m/s and km/h m/s. Multiply by to go back.
Distance is never less than the magnitude of displacement, and they are equal only for motion in a straight line without reversing. Use that as a check.
For a closed path, displacement is zero, so average velocity is zero while average speed is not.
A negative acceleration is just acceleration opposite to the motion — write *retardation of or acceleration of *, and do not treat them as different things.
Acceleration lies along the change in velocity, so a slowing car accelerates backwards.
Zero acceleration means constant velocity, not being at rest.
And write the unit on every answer: m/s for speed and velocity, for acceleration.
Did you know
Why the same journey has two honest answers
Ask two people how far it is from a house to a school and you can get two different numbers, both correct.
One answers km, meaning the road route — turn left, along the main road, right at the crossing. That is distance, and it is what a rickshaw driver charges for and what your shoes wear out over.
The other answers km, meaning the straight line across the fields. That is the magnitude of the displacement, and it is what a bird would fly and what a map measures with a ruler.
Neither is a mistake. They are answers to different questions, and physics keeps two separate words so the two questions cannot be confused.
The gap between them is a real measure of something — how indirect the route is. A journey along a straight road has distance equal to displacement, and the ratio is . A journey with one detour has a ratio a little above . And a journey that ends where it began has a displacement of zero, so the ratio becomes infinite — which is the mathematics saying, correctly, that no amount of straight-line progress was made however far you walked.
That last case is not a curiosity. A patrolling guard, a ceiling fan blade, a planet going round the Sun and an athlete finishing a lap all cover great distances with zero displacement, over and over. Their average speeds are large and their average velocities are zero, permanently.
So the two words are not a fussy distinction invented for examinations. They exist because how far did you go and how far away did you end up are genuinely different facts about the same journey, and any language for describing motion has to keep them apart.
One answers km, meaning the road route — turn left, along the main road, right at the crossing. That is distance, and it is what a rickshaw driver charges for and what your shoes wear out over.
The other answers km, meaning the straight line across the fields. That is the magnitude of the displacement, and it is what a bird would fly and what a map measures with a ruler.
Neither is a mistake. They are answers to different questions, and physics keeps two separate words so the two questions cannot be confused.
The gap between them is a real measure of something — how indirect the route is. A journey along a straight road has distance equal to displacement, and the ratio is . A journey with one detour has a ratio a little above . And a journey that ends where it began has a displacement of zero, so the ratio becomes infinite — which is the mathematics saying, correctly, that no amount of straight-line progress was made however far you walked.
That last case is not a curiosity. A patrolling guard, a ceiling fan blade, a planet going round the Sun and an athlete finishing a lap all cover great distances with zero displacement, over and over. Their average speeds are large and their average velocities are zero, permanently.
So the two words are not a fussy distinction invented for examinations. They exist because how far did you go and how far away did you end up are genuinely different facts about the same journey, and any language for describing motion has to keep them apart.
Exam relevance
How does this motion chapter feed into JEE and NEET Physics?
This page is the foundation for the Class 11 Physics chapter Motion in a Straight Line, and it is examined in JEE Main and in NEET Physics alike, since both include mechanics.
Distance against displacement becomes the formal scalar-and-vector distinction, and it leads directly into Class 11 Motion in a Plane, where displacement is handled by components rather than by a single sign. The right-angled triangle used in worked example 1 above is the first case of vector addition, and it is the same calculation done there with full notation.
Average speed against average velocity is one of the most reliably examined ideas in all of introductory mechanics. The two-stage journey — a distance at one speed followed by a distance at another — becomes a standard JEE Main numerical, often asked for two equal distances rather than equal times, which produces a harmonic mean rather than a simple average. That question exists precisely because averaging the two speeds is the intuitive and wrong move.
Average acceleration leads into the kinematic equations in the third part of this chapter, and then into Class 11 Laws of Motion, where makes acceleration the link between force and motion. Nothing in the rest of mechanics works without it.
The circular motion remark in the last section becomes centripetal acceleration in Class 11 Motion in a Plane, a recurring JEE Main topic.
What the questions look like. Numericals dominate: average speed over a multi-stage journey, displacement from a path described in words, acceleration from a velocity change with units to convert. Assertion-reason items are common, and a favourite pairs a body can have zero velocity and non-zero acceleration with a reason — a statement that is true at the top of a thrown ball's flight. Graph-based questions belong to the next part of this chapter.
How board and competitive emphasis differ. A board paper asks you to define average velocity or to state two differences between distance and displacement, and then sets a single-stage numerical. A competitive paper rarely asks for a definition; it builds a numerical in which the definition is the hidden step — most often by giving a journey whose average speed cannot be found by averaging. Board papers also accept km/h answers more readily, while competitive papers usually expect SI units throughout.
The single trap that costs the most marks. Averaging the two speeds instead of dividing total distance by total time. It is the same error whether the stages are given by time or by distance, and it is worth doing one of each by hand until the correct method is automatic.
A second trap worth naming. Treating retardation as a separate quantity with its own sign convention, and then writing for a body slowing down. There is one acceleration, and its sign tells you the direction relative to the motion — a confusion that produces wrong answers throughout the kinematic equations later.
Distance against displacement becomes the formal scalar-and-vector distinction, and it leads directly into Class 11 Motion in a Plane, where displacement is handled by components rather than by a single sign. The right-angled triangle used in worked example 1 above is the first case of vector addition, and it is the same calculation done there with full notation.
Average speed against average velocity is one of the most reliably examined ideas in all of introductory mechanics. The two-stage journey — a distance at one speed followed by a distance at another — becomes a standard JEE Main numerical, often asked for two equal distances rather than equal times, which produces a harmonic mean rather than a simple average. That question exists precisely because averaging the two speeds is the intuitive and wrong move.
Average acceleration leads into the kinematic equations in the third part of this chapter, and then into Class 11 Laws of Motion, where makes acceleration the link between force and motion. Nothing in the rest of mechanics works without it.
The circular motion remark in the last section becomes centripetal acceleration in Class 11 Motion in a Plane, a recurring JEE Main topic.
What the questions look like. Numericals dominate: average speed over a multi-stage journey, displacement from a path described in words, acceleration from a velocity change with units to convert. Assertion-reason items are common, and a favourite pairs a body can have zero velocity and non-zero acceleration with a reason — a statement that is true at the top of a thrown ball's flight. Graph-based questions belong to the next part of this chapter.
How board and competitive emphasis differ. A board paper asks you to define average velocity or to state two differences between distance and displacement, and then sets a single-stage numerical. A competitive paper rarely asks for a definition; it builds a numerical in which the definition is the hidden step — most often by giving a journey whose average speed cannot be found by averaging. Board papers also accept km/h answers more readily, while competitive papers usually expect SI units throughout.
The single trap that costs the most marks. Averaging the two speeds instead of dividing total distance by total time. It is the same error whether the stages are given by time or by distance, and it is worth doing one of each by hand until the correct method is automatic.
A second trap worth naming. Treating retardation as a separate quantity with its own sign convention, and then writing for a body slowing down. There is one acceleration, and its sign tells you the direction relative to the motion — a confusion that produces wrong answers throughout the kinematic equations later.
Key takeaways
Distance, displacement, speed and acceleration: quick revision
- Position needs a reference point, a positive direction and a distance. East as positive puts a post m east at m and a bench m west at m.
- Motion is relative: a bus passenger is at rest with respect to the bus and moving with respect to the road. In motion is incomplete without with respect to what.
- Distance is the whole path, a scalar, always positive. Displacement is the straight line from start to finish, a vector, and can be zero.
- m east then m north gives distance m and displacement m.
- m east then m west gives distance m and displacement m east.
- One lap of a m track gives distance m and displacement zero.
- km north then km east gives distance km and displacement km.
- Distance is never less than the magnitude of displacement, and they are equal only for a straight line without reversal.
- **Average speed ; average velocity .** Both in m/s.
- km/h m/s, so km/h m/s, km/h m/s, km/h m/s.
- The m and m walk in s and s gives average speed m/s and average velocity m/s east.
- km in h plus km in h gives km/h — not the average of and .
- Uniform motion covers equal distances in equal times, and then instantaneous speed equals average speed. A speedometer shows instantaneous speed.
- **Average acceleration **, in .
- Rest to m/s in s gives ; m/s to m/s in s gives , a retardation of .
- km/h to km/h in s means m/s to m/s, giving . Convert before substituting.
- Acceleration points along the change in velocity, so a slowing eastward car accelerates westward.
- Zero acceleration means constant velocity, not zero velocity — and a body moving in a circle at constant speed is accelerating.
Take one journey of your own with a turn and a return in it, and work out all four quantities — distance, displacement, average speed and average velocity — then check that the displacement came out smaller than the distance.
- Motion is relative: a bus passenger is at rest with respect to the bus and moving with respect to the road. In motion is incomplete without with respect to what.
- Distance is the whole path, a scalar, always positive. Displacement is the straight line from start to finish, a vector, and can be zero.
- m east then m north gives distance m and displacement m.
- m east then m west gives distance m and displacement m east.
- One lap of a m track gives distance m and displacement zero.
- km north then km east gives distance km and displacement km.
- Distance is never less than the magnitude of displacement, and they are equal only for a straight line without reversal.
- **Average speed ; average velocity .** Both in m/s.
- km/h m/s, so km/h m/s, km/h m/s, km/h m/s.
- The m and m walk in s and s gives average speed m/s and average velocity m/s east.
- km in h plus km in h gives km/h — not the average of and .
- Uniform motion covers equal distances in equal times, and then instantaneous speed equals average speed. A speedometer shows instantaneous speed.
- **Average acceleration **, in .
- Rest to m/s in s gives ; m/s to m/s in s gives , a retardation of .
- km/h to km/h in s means m/s to m/s, giving . Convert before substituting.
- Acceleration points along the change in velocity, so a slowing eastward car accelerates westward.
- Zero acceleration means constant velocity, not zero velocity — and a body moving in a circle at constant speed is accelerating.
Take one journey of your own with a turn and a return in it, and work out all four quantities — distance, displacement, average speed and average velocity — then check that the displacement came out smaller than the distance.